Normalize mix shader fac to .75 as midpoint instead of .5
ColorRamp (or RGBCurve) as Value Remapping Tool

While the transformation could be certainly achieved with several math nodes, I would suggest to take advantage of the ColorRamp node:


  The ColorRamp Node is used for mapping values to colors [and so to other values] with the use of a gradient.


The transformation you want to achieve is linear, with a different slope depending on which side of the range you fall into, but in any case is linear. We'll set up a Linear gradient for the node, then add a slider in corrispondece to the input value midpoint 


Pos = 0,5 in this case


and then set the value you would like to be mapped to


V = 0,75


This means that we are asking Blender to make a linear remap of the incoming value from black to white (0-1) with a midpoint (0,5) with a value of 0,75.



Note how this kind of set up should be done without Color Management models transforming your scene data. After that, you should be allowed to set it up like you want and everything should works fine. It's just an easy way to avoid being confused while seetting up the remapper.

Same thing can be done, and perhaps is visually more clear, with the RGBCurve node:



Values before the 0,5 point are change "faster" than the values that comes after. The midpoint has a new value of 0.75. You can change the handle type to Vector in the menu that appears once the wrench icon is clicked.

Here's a try with the values proposed at the end of the question: